This invention relates generally to spring washers and more particularly, to methods and apparatus for determining resilience of spring washers.
Conical spring washers are often used in fastening systems or support systems to insure that a compressive force is maintained on the clamped members throughout an intended service cycle. Once compressed, the conical spring washer continuously produces a force exerted on its immediately adjoining members (a separating force). When a conical spring washer is compressed between a bolt head or nut securing a clamped member and the clamped member, the separating force of the conical spring washer assists in clamping the clamped member. The spring washer""s effective operating travel produces and maintains a force on clamped members when there is differential movement (strain) between and among the clamped members and the clamping member, e.g., a bolt.
Spring washers are also used in applications to facilitate limiting an amount of movement of a component when the component experiences a failure or potentially failing event. For example, within a reactor pressure vessel (RPV) of a boiling water reactor (BWR), housing support rods below the RPV are contained within control rod housing supports that are coupled to the RPV using a plurality of spring washers and a nut. More specifically, the spring washers are positioned at the top end of the hanger support rods to facilitate limiting an amount of downward travel of the housing support rods in the event of a failure of the control rod drive housing.
Spring washers are typically used in such applications because the coned, annular-disk washers provide load-deflection characteristics that may not be readily obtainable with more conventional forms of springs. Accordingly, such washers are variably selected based on the number, arrangement, and characteristics of the spring washers used in such applications, and to facilitate optimizing each spring within an application, at least some known design formulas are used to determine suitable spring geometry characteristics. However, known formulas provide only limited characteristic accuracy because only known formulas only determine characteristics of one spring washer at a time. As such, to determine the characteristics of a stack of washers arranged in a series and/or parallel arrangement, numerous approximations must be made. Accordingly, spring characteristics based on such approximations may be inaccurate and may lead to failure of associated components.
In one aspect, a method for determining resilience of a plurality of spring washers stacked in a series arrangement is provided. The method comprises determining the potential energy for the series arrangement by integrating the product of the axial load applied to the series arrangement, the displacement of the series arrangement, and the number of spring washers stacked in the series arrangement, and solving at least two non-linear equations to determine the resilience of the spring washers stacked in the series arrangement.
In another aspect, an apparatus is provided for determining resilience of a plurality of spring washers stacked in a series arrangement. The apparatus includes a processor programmed to integrate the product of the axial load applied to the series arrangement, the displacement of the series arrangement, and the number of spring washers stacked in the series arrangement to determine the potential energy for the series arrangement, and solve at least two non-linear equations to determine the resilience of the spring washers stacked in the series arrangement.
In a further aspect of the invention, a system for determining resilience of a plurality of spring washers stacked in a series arrangement is provided. The system includes a client system including a browser, a data storage device for storing information relevant to a plurality of users, and a server system configured to be coupled to the client system and the data storage device. The server system is further configured to integrate the product of the axial load applied to the series arrangement, the displacement of the series arrangement, and the number of spring washers stacked in the series arrangement to determine the potential energy for the series arrangement, and to solve at least two non-linear equations to determine the resilience of the spring washers stacked in the series arrangement.